Space of modular forms of level 576, weight 3, and Character 576.b

• Label: 576.3.b
• Level: $576$
• Weight: $3$
• Character orbit: 576.b
• Rep. character: $\chi_{576}(415,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $288$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(288\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

	Total	New	Old
Modular forms	216	20	196
Cusp forms	168	20	148
Eisenstein series	48	0	48

Trace form

\( 20 q - 24 q^{17} - 172 q^{25} - 24 q^{41} - 108 q^{49} + 192 q^{65} - 88 q^{73} + 168 q^{89} - 536 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.3.b.a	$576$	$3$	576.b	8.d	$2$	$4$	$4$	$15.695$	\(\Q(\zeta_{12})\)	None					192.3.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}+5\beta_1 q^{7}-2\beta_{3} q^{11}-2\beta_{2} q^{13}+\cdots\)
576.3.b.b	$576$	$3$	576.b	8.d	$2$	$4$	$4$	$15.695$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		✓			576.3.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{5}-5\beta _{1}q^{7}+\beta _{3}q^{11}-71q^{25}+\cdots\)
576.3.b.c	$576$	$3$	576.b	8.d	$2$	$4$	$4$	$15.695$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			576.3.b.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_1 q^{7}+\beta_{2} q^{13}-\beta_{3} q^{19}+25 q^{25}+\cdots\)
576.3.b.d	$576$	$3$	576.b	8.d	$2$	$4$	$4$	$15.695$	\(\Q(\zeta_{12})\)	None					64.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}+\beta_{3} q^{7}-\beta_1 q^{11}+\beta_{2} q^{13}+\cdots\)
576.3.b.e	$576$	$3$	576.b	8.d	$2$	$4$	$4$	$15.695$	\(\Q(\zeta_{12})\)	None					192.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}-\beta_1 q^{7}+2\beta_{3} q^{11}+6\beta_{2} q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)